Mathematical Sciences: Linear Topological Properties of Certain Quasi-Banach Spaces of Analytic Functions

Eoff教授将研究两个函数空间的线性拓扑性质，这两个函数空间在其自然拓扑下被证明是拟巴拿赫空间。所涉及的主要问题之一是表征这些空间的巴拿赫包络。在其中一个空间的情况下，Eoff教授有一个猜想，她将试图验证。从许多角度来看，所涉及的空间是相当不寻常的，因为研究函数空间的数学家所熟悉的许多基本性质都不存在。然而，这些空间在分析某些类型的函数时自然出现，因此理解它们很重要。埃夫教授的研究将揭开这些空间的一些神秘面纱。这个项目是妇女研究机会活动的一部分。

Professor Eoff will study the linear topological properties of two spaces of functions which turn out to be quasi-Banach spaces under their natural topologies. One of the main problems involved is to characterize the Banach envelopes of these spaces. In the case of one of these spaces, Professor Eoff has a conjecture she will try to verify. The spaces involved are rather unusual from many points of view in that many of the basic properties familiar to mathematicians who work on function spaces are absent. However, these spaces arise naturally in the analysis of certain types of functions and thus are important to understand. Professor Eoff's research will remove some of the mystery surrounding these spaces. This project is part of the Research Opportunities for Women activity.